Hardness results for dynamic problems by extensions of Fredman and Saks' chronogram method

Husfeldt, Thore; Rauhe, Theis

doi:10.1007/bfb0055041

Cited by 5 publications

(5 citation statements)

References 29 publications

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“…This function is clearly in AC 0 , yet by (1) has large 'dynamic hardness' in the sense of Miltersen et al [33]. This contrasts the work in [27] were it is proved that for symmetric Boolean functions, there is a close correspondence between parallel and dynamic hardness.…”

Section: 7mentioning

confidence: 89%

“…The worst case lower bounds for the marked ancestor problem can be seen to hold even if we allow a model with nondeterministic queries as introduced in [27]. In short this model extends query computation with the additional power of accessing the data structure through nondeterministic guesses and such that positive query answers are verified in the usual sense.…”

Section: Variants and Extensionsmentioning

confidence: 99%

“…In short this model extends query computation with the additional power of accessing the data structure through nondeterministic guesses and such that positive query answers are verified in the usual sense. This should be contrasted with the fact that if T is a path, there is a provable gap between nondeterministic and deterministic query time as observed in [27], since nondeterminism allows worst case constant time complexity for firstmarked while supporting mark and unmark in worst case O(log log n) time. Furthermore, the existential marked ancestor problem has nondeterministic query algorithms that take constant time: guess a node on π(v) and verify that it is marked.…”

Section: Variants and Extensionsmentioning

confidence: 99%

“…Cell probe bounds for other geometric problems (point location) are given in [28,27], and some more can be seen to follow from [25].…”

Section: 7mentioning

confidence: 99%

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Marked Ancestor Problems (Preliminary Version)

Alstrup¹,

Husfeldt²,

Rauhe³

1998

BRICS

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Abstract. Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the well-known predecessor problem, where the tree is a path.We show tight upper and lower bounds for this problem. The lower bounds are proved in the cell probe model, the upper bounds run on a unit-cost RAM.As easy corollaries we prove (often optimal) lower bounds on a number of problems. These include planar range searching, including the existential or emptiness problem, priority search trees, static tree union-find, and several problems from dynamic computational geometry, including intersection problems, proximity problems, and ray shooting. Our upper bounds improve a number of algorithms from various fields, including dynamic dictionary matching and coloured ancestor problems.

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Section: 7mentioning

confidence: 89%

Section: Variants and Extensionsmentioning

confidence: 99%

Section: Variants and Extensionsmentioning

confidence: 99%

“…Cell probe bounds for other geometric problems (point location) are given in [28,27], and some more can be seen to follow from [25].…”

Section: 7mentioning

confidence: 99%

See 2 more Smart Citations

Marked Ancestor Problems (Preliminary Version)

Alstrup¹,

Husfeldt²,

Rauhe³

1998

BRICS

Self Cite

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“…certificates. The nondeterministic cell-probe complexity was studied for dynamic data structure problems in [5] and for static data structure problems in [19].…”

Section: Related Workmentioning

confidence: 99%

Certificates in Data Structures

Wang

Yin

2014

Automata, Languages, and Programming

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We study certificates in static data structures. In the cell-probe model, certificates are the cell probes which can uniquely identify the answer to the query. As a natural notion of nondeterministic cell probes, lower bounds for certificates in data structures immediately imply deterministic cell-probe lower bounds. In spite of this extra power brought by nondeterminism, we prove that two widely used tools for cell-probe lower bounds: richness lemma of Miltersen et al.[10] and direct-sum richness lemma of Pǎtraşcu and Thorup [17], both hold for certificates in data structures with even better parameters. Applying these lemmas and adopting existing reductions, we obtain certificate lower bounds for a variety of static data structure problems. These certificate lower bounds are at least as good as the highest known cell-probe lower bounds for the respective problems. In particular, for approximate near neighbor (ANN) problem in Hamming distance, our lower bound improves the state of the art. When the space is strictly linear, our lower bound for ANN in d-dimensional Hamming space becomes t = Ω(d), which along with the recent breakthrough for polynomial evaluation of Larsen [8], are the only two t = Ω(d) lower bounds ever proved for any problems in the cell-probe model.

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Cell-Probe Proofs and Nondeterministic Cell-Probe Complexity

Yin

2008

Automata, Languages and Programming

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Hardness results for dynamic problems by extensions of Fredman and Saks' chronogram method

Cited by 5 publications

References 29 publications

Marked Ancestor Problems (Preliminary Version)

Marked Ancestor Problems (Preliminary Version)

Certificates in Data Structures

Cell-Probe Proofs and Nondeterministic Cell-Probe Complexity

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